You do not give any information on where you are based. If you are a UK TV Licence payer, there is a huge amount of TV and radio programmes which can be legally down loaded using get-iplayer. It is quicker and easier to use this to download BBC programmes than it is to use tvheadend and the TVHat. Some ITV programmes can be downloaded from the ITVHub using youtube-dl. Programmes from the Channel 4 family and the UK Freeview family can be watched (rather than copied) on other platforms using the Adobe Flash Player but I have not been able to run them on my Raspberry Pi. I have not made much effort to do so since there are so many other programmes I can watch. These programmes can, of course, be downloaded using tvheadend and the TVHat. As far as I know, tvheadend is the only Personal Video Recorder (PVR) which is relatively easy to set up and use on Raspbian . I have never seriously looked at Kodi and other operating systems . You might decide otherwise.
I have had no problems in setting up and using my Seagate 2 TB drive which is powered by a Pi USB socket. You would have to set an output for your destination files; mine is -o /media/pi/USBdisc/TV/filename. If you download the Minimal Kiosk Browser you get a very useful browser which can be dedicated for specific tasks but also a very useful media player called omxplayergui which can be set up to show various categories of media and play them. Omxplayergui works independently of the Minimal Kiosk Browser and does not need it to be running. An enhanced and accelerated verstion of the VLC Media Player is now automatically added to new downloads of Raspbian and this is very useful for playing and displaying live TV programmes. Programme lists can be set up in .m3u text files.